A numerical method for computing the structured singular value
The article is devoted to a numerical testing procedure for the robustness of systems whose performances can be expressed as \(\| F(z)\|\), where \(z\in M_{tr}\) contains uncertain parameters and for given matrices \(a\in M_{lk}\), \(b\in M_{lt}\), \(c\in M_{rk}\), \(d\in M_{rt}\), F is defined as \[ F_{\left( \begin{matrix} a\quad b\\ c\quad d\end{matrix} \right)}(z)=a+bz(I+dz)^{-1}c. \] The plant uncertainty problem is to verify if for given \(\left( \begin{matrix} a\quad b\\ c\quad d\end{matrix} \right)\) a simplex \(\Omega \subset M_{tr}\) and \(\rho >0\) the inequality \(\| F_{\left( \begin{matrix} a\quad b\\ c\quad d\end{matrix} \right)}(z)\| <\rho\) remains true for all \(z\in \Omega\). The proposed algorithm is based on transforming the initial problem in two subproblems: the first step is equivalent to a quadratic programming approach and the second needs to find the highest eigenvalue of a matrix.
scientific article; zbMATH DE number 4066246